In [3]: 
import sys
sys.setrecursionlimit(10000)
import warnings
warnings.filterwarnings('ignore', category=DeprecationWarning)

import os
os.environ['GNUMPY_IMPLICIT_CONVERSION'] = 'allow'
print os.environ.get('GNUMPY_IMPLICIT_CONVERSION')

allow
In [29]: 
import cPickle
import gzip

from breze.learn.data import one_hot
from breze.learn.base import cast_array_to_local_type
from breze.learn.utils import tile_raster_images

import climin.stops
import climin.initialize
from climin import mathadapt as ma

from breze.learn import hvi
from breze.learn.hvi import HmcViModel
from breze.learn.hvi.energies import (NormalGaussKinEnergyMixin, DiagGaussKinEnergyMixin, MlpDiagGaussKinEnergyMixin)
from breze.learn.hvi.inversemodels import MlpGaussInvModelMixin, MlpInvAcceptProbModelMixin, UniformInvModelMixin

from matplotlib import pyplot as plt
from matplotlib import cm

import numpy as np
from scipy.stats import norm as normal_distribution

#import fasttsne

from IPython.html import widgets
%matplotlib inline

import theano
theano.config.compute_test_value = 'ignore'#'raise'
from theano import (tensor as T, clone)
In [4]: 
datafile = '../mnist.pkl.gz'
# Load data.                                                                                                   

with gzip.open(datafile,'rb') as f:                                                                        
    train_set, val_set, test_set = cPickle.load(f)                                                       

X, Z = train_set                                                                                               
VX, VZ = val_set
TX, TZ = test_set

Z = one_hot(Z, 10)
VZ = one_hot(VZ, 10)
TZ = one_hot(TZ, 10)

X_no_bin = X
VX_no_bin = VX
TX_no_bin = TX

# binarize the MNIST data
np.random.seed(0)
VX = np.random.binomial(1, np.tile(VX, (5, 1))) * 1.0
TX = np.random.binomial(1, np.tile(TX, (5, 1))) * 1.0
X  = np.random.binomial(1, X) * 1.0

print VX.shape

image_dims = 28, 28

X_np, Z_np, VX_np, VZ_np, TX_np, TZ_np, X_no_bin_np, VX_no_bin_np, TX_no_bin_np = X, Z, VX, VZ, TX, TZ, X_no_bin, VX_no_bin, TX_no_bin
X, Z, VX, VZ, TX, TZ, X_no_bin, VX_no_bin, TX_no_bin = [cast_array_to_local_type(i) 
                                                        for i in (X, Z, VX,VZ, TX, TZ, X_no_bin, VX_no_bin, TX_no_bin)]
print X.shape

(50000L, 784L)
(50000L, 784L)


\\srv-file.brml.tum.de\nthome\cwolf\code\2015-christopherwolf-msc\breze\learn\base.py:39: UserWarning: Implicilty converting numpy.ndarray to gnumpy.garray
  warnings.warn('Implicilty converting numpy.ndarray to gnumpy.garray')
In [5]: 
fig, ax = plt.subplots(figsize=(9, 9))

img = tile_raster_images(X_np[:64], image_dims, (8, 8), (1, 1))
ax.imshow(img, cmap=cm.binary)
Out[5]:
<matplotlib.image.AxesImage at 0x27386828>
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [45]: 
fast_dropout = False

if fast_dropout:
    class MyHmcViModel(HmcViModel, 
                   hvi.FastDropoutMlpBernoulliVisibleVAEMixin, 
                   hvi.FastDropoutMlpGaussLatentVAEMixin, 
                   DiagGaussKinEnergyMixin,
                   MlpGaussInvModelMixin):
        pass

    kwargs = {
        'p_dropout_inpt': .1,
        'p_dropout_hiddens': [.2, .2],
    }

    print 'yeah'

else:
    class MyHmcViModel(HmcViModel, 
                   hvi.MlpBernoulliVisibleVAEMixin, 
                   hvi.MlpGaussLatentVAEMixin, 
                   DiagGaussKinEnergyMixin,  # MlpDiagGaussKinEnergyMixin, DiagGaussKinEnergyMixin
                   UniformInvModelMixin): # MlpGaussInvModelMixin, MlpInvAcceptProbModelMixin
        pass
    kwargs = {}


batch_size = 500
#optimizer = 'rmsprop', {'step_rate': 1e-4, 'momentum': 0.95, 'decay': .95, 'offset': 1e-6}
#optimizer = 'adam', {'step_rate': .5, 'momentum': 0.9, 'decay': .95, 'offset': 1e-6}
optimizer = 'adam', {'step_rate': 0.001}

# This is the number of random variables NOT the size of 
# the sufficient statistics for the random variables.
n_latents = 2
n_hidden = 200

m = MyHmcViModel(X.shape[1], n_latents, 
                 [n_hidden, n_hidden], ['softplus'] * 2, 
                 [n_hidden, n_hidden], ['rectifier'] * 2, 
                 [n_hidden, n_hidden], ['rectifier'] * 2,
                 n_hmc_steps=3, n_lf_steps=4,
                 n_z_samples=1,
          optimizer=optimizer, batch_size=batch_size, allow_partial_velocity_update=False, perform_acceptance_step=False,
          compute_transition_densities=False, consider_aux_inv_model_inpt_constant=False,
          **kwargs)

climin.initialize.randomize_normal(m.parameters.data, 0.1, 1e-1)
#m.parameters.__setitem__(m.hmc_sampler.step_size_param, 0.2)
#m.parameters.__setitem__(m.kin_energy.mlp.layers[-1].bias, 1)
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [46]: 
old_best_params = None
#print m.score(TX)
print m.parameters.data.shape

(396391,)
In [47]: 
FILENAME = 'hvi_gen2_recog2_aux2_late2_hid200_pretr_3hmc_04lf_uniformauxnotrans.pkl'

# In[5]:
#old_best_params = None
f = open(FILENAME, 'rb')
np_array = cPickle.load(f)
old_best_params = cast_array_to_local_type(np_array)
f.close()
print old_best_params.shape

(396391L,)
In [48]: 
m.parameters.data = old_best_params.copy()
#old_best_loss = m.score(VX)
#print old_best_loss
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [49]: 
print m.score(VX)
print m.score(TX)
print m.score(X[:50000])

compiled score function
garray(125.15157318115234)
garray(125.98513793945312)
garray(123.6635971069336)
In [19]: 
print m.parameters.view(m.init_recog.mlp.layers[2].bias)

garray([ 0.01572736,  0.25879094,  0.2682229 ,  0.02873316,  0.01132663,
         0.14681463,  0.39507347, -0.00952354, -0.40507248,  0.24143711,
         0.04885972, -0.00555071, -0.22508289,  0.17706092,  0.0016573 ,
         0.28451693,  0.38109457, -0.12790132, -0.43630773, -0.4849095 ,
        -0.60470414, -0.30611604, -0.12809692, -0.62439138, -0.88191092,
        -0.29111061, -0.16776907, -0.92417669, -0.19506952, -0.07011253,
        -0.08524222, -0.16235654, -0.05174336, -0.34162965, -0.39058596,
        -0.0801597 , -0.44442758, -0.24635278, -0.49210778, -0.44178995])
In [28]: 
#m.parameters.__setitem__(m.hmc_sampler.step_size_param, m.parameters.view(m.hmc_sampler.step_size_param) * np.sqrt(3.0))
#m.parameters.__setitem__(m.init_recog.mlp.layers[2].bias, cast_array_to_local_type(np.array([ 0.14096579,  0.53084856, -1.75648117, -2.5653615 ])))
#m.parameters.__setitem__(m.kin_energy.variance_parameter, cast_array_to_local_type(-0.7*np.ones_like(m.kin_energy.variance_parameter)))
In [11]: 
print 0.1 * m.parameters.view(m.hmc_sampler.step_size_param) ** 2 + 1e-8

garray([ 0.00419771])
In [21]: 
print m.parameters.view(m.hmc_sampler.partial_velocity_parameter)
print np.tanh(m.parameters.view(m.hmc_sampler.partial_velocity_parameter))

garray([ 0.37883562])
[ 0.36169584]
In [71]: 
print m.estimate_nll(TX, 5000) # n=1000: 87.741, 87.747; n=2000: 87.674; n=2500: 87.655; n=5000: 87.601

126.743628814
In [None]: 
print m.estimate_nll_MCMC(TX[:100], 500, 100, 0.01)
In [9]: 
# Convert to numpy array
f = open(FILENAME + '_np.pkl', 'wb')
cPickle.dump(m.parameters.data.as_numpy_array(), f, protocol=cPickle.HIGHEST_PROTOCOL)
f.close()
In [1]: 
m._f_loss, m._f_dloss = m._make_loss_functions()

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-1-91597f2ec9d6> in <module>()
----> 1 m._f_loss, m._f_dloss = m._make_loss_functions()

NameError: name 'm' is not defined
In [None]: 
if False:
    full_f_dloss = m._f_dloss
    only_aux_inv_mask = np.zeros_like(m.parameters.data)
    for i in range(3):
        auxiliary_inv_weight_param_range = m.parameters._var_to_slice[m.auxiliary_inv_model.mlp.layers[i].weights]
        auxiliary_inv_bias_param_range = m.parameters._var_to_slice[m.auxiliary_inv_model.mlp.layers[i].bias]
        print auxiliary_inv_weight_param_range, auxiliary_inv_bias_param_range
        only_aux_inv_mask[slice(*auxiliary_inv_weight_param_range)] = 1.0
        only_aux_inv_mask[slice(*auxiliary_inv_bias_param_range)] = 1.0

    def only_aux_inv_loss(params, data, *args):
        return cast_array_to_local_type(only_aux_inv_mask) * full_f_dloss(params, data, *args)

    m._f_dloss = only_aux_inv_loss
In [None]: 
from theano.printing import debugprint
#debugprint(m._f_dloss.theano_func)
In [None]: 
print m.parameters._var_to_shape
print
print m.parameters._var_to_slice
In [None]: 
grad_array = np.zeros((100, len(m.parameters.data)))
for i in range(100):
    grad_array[i, :] = m._f_dloss(m.parameters.data, X[:625])
In [None]: 
mean_grad = grad_array.mean(axis=0)
print abs(mean_grad).mean()
print mean_grad.min(), mean_grad.argmin()
print mean_grad.max(), mean_grad.argmax()

# 0.0068310414746
# -8.18554486275 196327
# 14.5694446664 197230
In [None]: 
x = (abs(mean_grad) > 5).astype('int32')
matchings_indices = [ i for i, value in enumerate(x) if value == 1 ]
print matchings_indices
# [196327, 197226, 197230, 197270, 197450, 197566, 197750, 197862, 197866, 197938]
In [None]: 
std_grad = grad_array.std(axis=0)
print std_grad.mean()
print std_grad.min(), std_grad.argmin()
print std_grad.max(), std_grad.argmax()
print mean_grad[std_grad.argmax()]

# 0.0173799498656
# 0.0 2
# 179.490609337 197230
# 14.5694446664
In [None]: 
print (abs(mean_grad) > 1).sum()
print (abs(mean_grad) > 2).sum()
print (abs(mean_grad) > 10).sum()
# 310
# 55
# 2
In [None]: 
consconst_mean_grad = mean_grad
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [None]: 
TARGET_FILENAME = 'hvi_gen2_recog2_aux2_late2_hid200_pretr_3hmc_04lf_accept_with_prob'
FILETYPE_EXTENSION = '.pkl'
old_best_params = None

m.optimizer = 'adam', {'step_rate': 0.0001}

max_passes = 200
max_iter = max_passes * X.shape[0] / batch_size
n_report = X.shape[0] / batch_size

stop = climin.stops.AfterNIterations(max_iter)
pause = climin.stops.ModuloNIterations(n_report)

# theano.config.optimizer = 'fast_compile'

for i, info in enumerate(m.powerfit((X_no_bin,), (VX,), stop, pause, eval_train_loss=False)):
    print i, m.score(X[:10000]).astype('float32'), info['val_loss'], np.exp(m.parameters.view(m.kin_energy.variance_parameter).as_numpy_array()), 0.1*m.parameters.view(m.hmc_sampler.step_size_param).as_numpy_array()**2 + 1e-8
    if i == 0 and old_best_params is not None:
        if info['best_loss'] > old_best_loss:
            info['best_loss'] = old_best_loss
            info['best_pars'] = old_best_params
    
    if info['best_loss'] == info['val_loss']:
        f = open(TARGET_FILENAME + FILETYPE_EXTENSION, 'wb')
        cPickle.dump(m.parameters.data, f, protocol=cPickle.HIGHEST_PROTOCOL)
        f.close()
In [None]: 
train_result_params = m.parameters.data.copy()
#m.parameters.data = info['best_pars']
#m.score(VX)
In [None]: 
m.parameters.data = train_result_params
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [50]: 
f_z_init_sample = m.function(['inpt'], m.init_recog.sample(), numpy_result=True)
f_z_sample = m.function(['inpt'], m.hmc_sampler.output, numpy_result=True)
f_gen = m.function([m.gen.inpt], m.gen.sample(), numpy_result=True)
f_gen_rate = m.function([m.gen.inpt], m.gen.rate, numpy_result=True)
f_joint_nll = m.function(['inpt'], m.joint_nll, numpy_result=True)
In [51]: 
curr_pos = T.matrix('current_position')
curr_vel = T.matrix('current_velocity')
norm_noise = T.matrix('normal_noise')
unif_noise = T.vector('uniform_noise')

new_sampled_vel = m.hmc_sampler.kin_energy.sample(norm_noise)
updated_vel = m.hmc_sampler.partial_vel_constant * curr_vel + m.hmc_sampler.partial_vel_complement * new_sampled_vel
performed_hmc_steps = m.hmc_sampler.perform_hmc_steps(curr_pos, curr_vel)
hmc_step = m.hmc_sampler.hmc_step(curr_pos, curr_vel, np.float32(0), norm_noise, unif_noise)
lf_step_results = m.hmc_sampler.simulate_dynamics(curr_pos, curr_vel, return_full_list=True)

f_pot_en = m.function(['inpt', curr_pos], m.hmc_sampler.eval_pot_energy(curr_pos), numpy_result=True)
f_kin_en = m.function(['inpt', curr_vel], m.kin_energy.nll(curr_vel).sum(-1), numpy_result=True)
f_perform_hmc_steps = m.function(['inpt', curr_pos, curr_vel], 
                                T.concatenate([performed_hmc_steps[0], performed_hmc_steps[1]], axis=1))
f_hmc_step = m.function(['inpt', curr_pos, curr_vel, norm_noise, unif_noise], 
                        T.concatenate([hmc_step[0], hmc_step[1]],axis=1), on_unused_input='warn')
f_kin_energy_sample_from_noise = m.function(['inpt', norm_noise], new_sampled_vel)
f_updated_vel_from_noise = m.function(['inpt', curr_vel, norm_noise], updated_vel)
f_perform_lf_steps = m.function(['inpt', curr_pos, curr_vel],
                               T.concatenate([lf_step_results[0], lf_step_results[1]], axis=0))

\\srv-file.brml.tum.de\nthome\cwolf\code\2015-christopherwolf-msc\breze\arch\util.py:630: UserWarning: theano.function was asked to create a function computing outputs given certain inputs, but the provided input variable at index 5 is not part of the computational graph needed to compute the outputs: uniform_noise-for-gpu.
To make this warning into an error, you can pass the parameter on_unused_input='raise' to theano.function. To disable it completely, use on_unused_input='ignore'.
  on_unused_input=on_unused_input, updates=updates)
In [88]: 
z1_by_z0_0 = T.grad(lf_step_results[0][-1, 0, 0], curr_pos)
z1_by_z0_1 = T.grad(lf_step_results[0][-1, 0, 1], curr_pos)
z1_by_z0 = T.concatenate([z1_by_z0_0, z1_by_z0_1], axis=0)
f_z1_by_z0 = m.function(['inpt', curr_pos, curr_vel], z1_by_z0, numpy_result=True, on_unused_input='warn')

zT_by_z0_0 = T.grad(performed_hmc_steps[0][-1, 0, 0], curr_pos)
zT_by_z0_1 = T.grad(performed_hmc_steps[0][-1, 0, 1], curr_pos)
zT_by_z0 = T.concatenate([zT_by_z0_0, zT_by_z0_1], axis=0)
f_zT_by_z0 = m.function(['inpt', curr_pos, curr_vel], zT_by_z0, numpy_result=True, on_unused_input='warn')
In [52]: 
f_z_init_mean = m.function(['inpt'], m.init_recog.mean, numpy_result=True)
f_z_init_var = m.function(['inpt'], m.init_recog.var, numpy_result=True)

f_v_init_var = m.function(['inpt'], T.extra_ops.cpu_contiguous(m.kin_energy.var), numpy_result=True)

full_sample = m.hmc_sampler.sample_with_path()
f_full_sample = m.function(['inpt'], T.concatenate([full_sample[0], full_sample[1]], axis=1))
In [90]: 
pos = T.matrix('pos')
vel = T.matrix('vel')
updated_vel = T.matrix('updated_vel')
time_step = T.vector('time_step')

aux_inpt_replacements = {m.auxiliary_inv_model_inpt['position']: pos, 
                         m.auxiliary_inv_model_inpt['time']: T.cast(time_step[0], dtype='float32')}
if 'velocity' in m.auxiliary_inv_model_inpt:  # only use the updated velocity if it is part of the model
    aux_inpt_replacements.update({m.auxiliary_inv_model_inpt['velocity']: updated_vel})

aux_inv_model_var = clone(m.auxiliary_inv_model.var, replace=aux_inpt_replacements)
aux_inv_model_mean = clone(m.auxiliary_inv_model.mean, replace=aux_inpt_replacements)
aux_inv_model_nll = clone(m.auxiliary_inv_model.nll(vel).sum(-1), replace=aux_inpt_replacements)

if 'velocity' not in m.auxiliary_inv_model_inpt:
    f_aux_inv_var = m.function(['inpt', pos, time_step], aux_inv_model_var, numpy_result=True)
    f_aux_inv_mean = m.function(['inpt', pos, time_step], aux_inv_model_mean, numpy_result=True)
    f_aux_inv_nll = m.function(['inpt', pos, time_step, vel], aux_inv_model_nll, numpy_result=True)
else:
    f_aux_inv_var = m.function(['inpt', pos, updated_vel, time_step], aux_inv_model_var, numpy_result=True)
    f_aux_inv_mean = m.function(['inpt', pos, updated_vel, time_step], aux_inv_model_mean, numpy_result=True)
    f_aux_inv_nll = m.function(['inpt', pos, updated_vel, time_step, vel], aux_inv_model_nll, numpy_result=True)
        
final_vel_inpt_replacements = {m.final_vel_model_inpt['position']: pos, 
                               m.final_vel_model_inpt['time']: T.cast(m.n_hmc_steps, dtype='float32')}

final_vel_model_var = clone(m.final_vel_model.var, replace=final_vel_inpt_replacements)
final_vel_model_mean = clone(m.final_vel_model.mean, replace=final_vel_inpt_replacements)
final_vel_model_nll = clone(m.final_vel_model.nll(vel).sum(-1), replace=final_vel_inpt_replacements)

f_v_final_var = m.function(['inpt', pos], final_vel_model_var, numpy_result=True)
f_v_final_mean = m.function(['inpt', pos], final_vel_model_mean, numpy_result=True)
f_v_final_model_nll = m.function(['inpt', pos, vel], final_vel_model_nll, numpy_result=True)

f_kin_energy_nll = m.function(['inpt'], m.kin_energy.expected_nll, numpy_result=True)
In [53]: 
f_init_recog_nll = m.function(['inpt'], m.init_recog.expected_nll.sum(-1), numpy_result=True)
In [None]: 
pos = T.matrix()
f_pot_en_deriv = m.function(['inpt', pos], m.hmc_sampler.eval_pot_energy_deriv(pos))
f_pot_en_2nd_deriv0 = m.function(['inpt', m.hmc_sampler.pot_energy_inpt], T.grad(m.hmc_sampler.pot_energy_deriv[0, 0], m.hmc_sampler.pot_energy_inpt))
f_pot_en_2nd_deriv1 = m.function(['inpt', m.hmc_sampler.pot_energy_inpt], T.grad(m.hmc_sampler.pot_energy_deriv[0, 1], m.hmc_sampler.pot_energy_inpt))
In [54]: 
print f_init_recog_nll(VX).mean()
init_var = f_z_init_var(VX)
print init_var.mean()
print init_var.max()
print init_var.min()
print
print f_joint_nll(TX).mean()

-2.27755
0.00730283
0.0696116
7.00209e-05

123.678
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [55]: 
fig, axs = plt.subplots(2, 3, figsize=(27, 18))

### Original data

O = (X_no_bin_np[:64])[:, :784].astype('float32')
img = tile_raster_images(O, image_dims, (8, 8), (1, 1))
axs[0, 0].imshow(img, cmap=cm.binary)

O2 = (X_np[:64])[:, :784].astype('float32')
img = tile_raster_images(O2, image_dims, (8, 8), (1, 1))
axs[1, 0].imshow(img, cmap=cm.binary)

### Reconstruction

#z_sample = f_z_sample((X[:64]))
z_init_sample = cast_array_to_local_type(f_z_init_sample((X[:64])))
z_sample = f_perform_hmc_steps((X[:64]), 
                               z_init_sample, 
                               f_kin_energy_sample_from_noise((X[:64]), 
                                                              cast_array_to_local_type(np.random.normal(size=(64, m.n_latent)).astype('float32')))
                               )[-1, :64, :]

R = f_gen_rate(z_sample)[:, :784].astype('float32')
img = tile_raster_images(R, image_dims, (8, 8), (1, 1))
axs[0, 1].imshow(img, cmap=cm.binary)

Rinit = f_gen_rate(z_init_sample)[:, :784].astype('float32')
img = tile_raster_images(Rinit, image_dims, (8, 8), (1, 1))
axs[0, 2].imshow(img, cmap=cm.binary)

R2 = f_gen(z_sample)[:, :784].astype('float32')
img = tile_raster_images(R2, image_dims, (8, 8), (1, 1))
axs[1, 1].imshow(img, cmap=cm.binary)

Rinit2 = f_gen(z_init_sample)[:, :784].astype('float32')
img = tile_raster_images(Rinit2, image_dims, (8, 8), (1, 1))
axs[1, 2].imshow(img, cmap=cm.binary)
Out[55]:
<matplotlib.image.AxesImage at 0x7afba240>
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [56]: 
fig, axs = plt.subplots(1, 2, figsize=(18, 9))

prior_sample = cast_array_to_local_type(np.random.randn(64, m.n_latent))

S = f_gen_rate(prior_sample)[:, :784].astype('float32')
img = tile_raster_images(S, image_dims, (8, 8), (1, 1))
axs[0].imshow(img, cmap=cm.binary)

S2 = f_gen(prior_sample)[:, :784].astype('float32')
img = tile_raster_images(S2, image_dims, (8, 8), (1, 1))
axs[1].imshow(img, cmap=cm.binary)

#S3 = f_gen_rate(prior_sample)[:, :784].astype('float32')
#img = tile_raster_images(S, image_dims, (8, 8), (1, 1))
#axs[2, 2].imshow(img, cmap=cm.nipy_spectral)
Out[56]:
<matplotlib.image.AxesImage at 0x7409a860>
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [57]: 
dim1 = 0
dim2 = 1
In [58]: 
from scipy.stats import norm as normal_distribution

unit_interval_positions = np.linspace(0.025, 0.975, 20)
positions = normal_distribution.ppf(unit_interval_positions)
print unit_interval_positions
print positions

latent_array = np.zeros((400, m.n_latent))
latent_array[:, dim2] = -np.repeat(positions, 20)  # because images are filled top -> bottom, left -> right (row by row)
latent_array[:, dim1] = np.tile(positions, 20)
        
fig, axs = plt.subplots(1, 1, figsize=(24, 24))

F = f_gen_rate(cast_array_to_local_type(latent_array)).astype('float32')

img = tile_raster_images(F, image_dims, (20, 20), (1, 1))
#axs.imshow(img, cmap=cm.nipy_spectral)
axs.imshow(img, cmap=cm.binary)

[ 0.025  0.075  0.125  0.175  0.225  0.275  0.325  0.375  0.425  0.475
  0.525  0.575  0.625  0.675  0.725  0.775  0.825  0.875  0.925  0.975]
[-1.95996398 -1.43953147 -1.15034938 -0.93458929 -0.75541503 -0.59776013
 -0.45376219 -0.31863936 -0.18911843 -0.06270678  0.06270678  0.18911843
  0.31863936  0.45376219  0.59776013  0.75541503  0.93458929  1.15034938
  1.43953147  1.95996398]
Out[58]:
<matplotlib.image.AxesImage at 0x525da4a8>
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [59]: 
data_set = 'train'  # 'train', 'validation', 'test'

if data_set == 'train':
    L = f_z_sample(X)
    L_init = f_z_init_sample(X)
    class_vec = Z[:].argmax(1)
elif data_set == 'validation':
    L = f_z_sample(VX)
    L_init = f_z_init_sample(VX)
    class_vec = VZ[:].argmax(1)
elif data_est == 'test':
    L = f_z_sample(TX)
    L_init = f_z_init_sample(TX)
    class_vec = TZ[:].argmax(1)
else:
    print 'unknown data set, must be one of: train, validation, test'
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [60]: 
dim1 = 0
dim2 = 1
In [61]: 
fig, axs = plt.subplots(1, 2, figsize=(18, 9))

normal_cdf_rescale = True

if normal_cdf_rescale:
    end_points = normal_distribution.cdf(L)
    init_points = normal_distribution.cdf(L_init)
else:
    end_points = L
    init_points = L_init

axs[0].scatter(end_points[:, dim1], end_points[:, dim2], c=class_vec, lw=0, s=10, alpha=.4)
axs[1].scatter(init_points[:, dim1], init_points[:, dim2], c=class_vec, lw=0, s=10, alpha=.4)

cax = fig.add_axes([0.95, 0.2, 0.02, 0.6])
cax.scatter(np.repeat(0, 10), np.arange(10), c=np.arange(10), lw=0, s=300)
cax.set_xlim(-0.1, 0.1)
cax.set_ylim(-0.5, 9.5)
plt.yticks(np.arange(10))
plt.tick_params(axis='x', which='both', bottom='off', top='off', labelbottom='off')
cax.tick_params(axis='y', colors='white')
for tick in cax.yaxis.get_major_ticks():
    tick.label.set_fontsize(14)
    tick.label.set_color('black')
    
cax.spines['bottom'].set_color('white')
cax.spines['top'].set_color('white') 
cax.spines['right'].set_color('white')
cax.spines['left'].set_color('white')

axs[0].set_title('After HMC steps')
axs[1].set_title('Initial recognition model')

if normal_cdf_rescale:
    axs[0].set_xlim(0, 1)
    axs[0].set_ylim(0, 1)
    axs[1].set_xlim(0, 1)
    axs[1].set_ylim(0, 1)
else:
    axs[0].set_xlim(-3, 3)
    axs[0].set_ylim(-3, 3)
    axs[1].set_xlim(-3, 3)
    axs[1].set_ylim(-3, 3)
In [62]: 
if n_latents == 2:
    if normal_cdf_rescale:
        fig, axs = plt.subplots(1, 1, figsize=(24, 24))

        F = f_gen_rate(cast_array_to_local_type(latent_array)).astype('float32')
        img = tile_raster_images(F, image_dims, (20, 20), (1, 1))
        #axs.imshow(img, cmap=cm.nipy_spectral)
        axs.imshow(img, cmap=cm.binary)
        axs.scatter(578.0*end_points[:, dim1], 578.0*(1 - end_points[:, dim2]), c=class_vec, lw=0, s=10, alpha=0.7)

        axs.set_xlim([0, 578])
        axs.set_ylim([578, 0])
    else:
        print 'Currently only available, if the scatter plot used rescaling by the normal CDF.'
        print 'Set normal_cdf_rescale=True in the previous cell'
In [63]: 
fig, axs = plt.subplots(4, 5, figsize=(20, 16))
colors = cm.jet(np.linspace(0, 1, 10))
for i in range(5):
    axs[0, i].scatter(init_points[Z[:].argmax(1) == i, dim1], init_points[class_vec == i, dim2], c=colors[i], lw=0, s=5, alpha=.2)
    axs[1, i].scatter(end_points[Z[:].argmax(1) == i, dim1], end_points[class_vec == i, dim2], c=colors[i], lw=0, s=5, alpha=.2)
    axs[0, i].set_title(str(i) + ' before HMC')
    axs[1, i].set_title(str(i) + ' after HMC')
    axs[2, i].scatter(init_points[Z[:].argmax(1) == (5+i), dim1], init_points[class_vec == (5+i), dim2], c=colors[5+i], lw=0, s=5, alpha=.2)
    axs[3, i].scatter(end_points[Z[:].argmax(1) == (5+i), dim1], end_points[class_vec == (5+i), dim2], c=colors[5+i], lw=0, s=5, alpha=.2)
    axs[2, i].set_title(str(5+i) + ' before HMC')
    axs[3, i].set_title(str(5+i) + ' after HMC')
    for j in range(4):
        if normal_cdf_rescale:
            axs[j, i].set_xlim(0, 1)
            axs[j, i].set_ylim(0, 1)
        else:
            axs[j, i].set_xlim(-3, 3)
            axs[j, i].set_ylim(-3, 3)
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [64]: 
X_index = 2  # index=0 -> 5, index=1 -> 0, index=2 -> 4, index=3 -> 1, index=24 -> underlined 1, index=39 -> ugly 6
from_data_set = X
from_data_set_no_bin = X_no_bin
num_repeats = 1000

X_array = np.array([from_data_set[X_index, :]]).astype('float32')
X_array_no_bin = np.array([from_data_set_no_bin[X_index % (from_data_set_no_bin.shape[0]), :]]).astype('float32')
fig, axs = plt.subplots(1, 2, figsize=(6, 3))

img = tile_raster_images(X_array, image_dims, (1, 1), (1, 1))
axs[0].imshow(img, cmap=cm.binary)
img = tile_raster_images(X_array_no_bin, image_dims, (1, 1), (1, 1))
axs[1].imshow(img, cmap=cm.binary)
Out[64]:
<matplotlib.image.AxesImage at 0x73d48c50>
In [65]: 
repeated_X = cast_array_to_local_type(np.tile(X_array, (num_repeats, 1)))

full_sample = f_full_sample(repeated_X).astype('float32')
z_samples = full_sample[:, :num_repeats, :]
v_samples = full_sample[:, num_repeats:, :]

z_sample_mean = z_samples[:, :, :].mean(axis=1)
z_sample_std = z_samples[:, :, :].std(axis=1)

single_X = cast_array_to_local_type(X_array)
init_mean = f_z_init_mean(single_X)[0]
init_var = f_z_init_var(single_X)[0]

init_vel_var = f_v_init_var(single_X)[0]

print 'Posterior distribution statistics'
print
print 'Initial model: - Mean: ' + str(init_mean)
print '               - Var:  ' + str(init_var)
print
print 'Full HVI model: - Mean: ' + str(z_sample_mean[m.n_hmc_steps])
print '                - Var:  ' + str(z_sample_std[m.n_hmc_steps] ** 2)
print
print 'Velocity model variance: ' + str(init_vel_var)

Posterior distribution statistics

Initial model: - Mean: [-2.41008377  1.30305839]
               - Var:  [ 0.00520702  0.01294701]

Full HVI model: - Mean: [-2.44337821  1.21974301]
                - Var:  [ 0.00428093  0.00053101]

Velocity model variance: [ 0.42712072  0.46283826]
In [66]: 
mean_loss = m.score(repeated_X).mean()
print 'Mean loss for this X: ', mean_loss

single_z_evolution = z_samples[:, 0, :]

R = f_gen_rate(cast_array_to_local_type(single_z_evolution)).astype('float32')

num_steps = m.n_hmc_steps + 1
num_images = num_steps + 1
fig, axs = plt.subplots(1, num_images, figsize=(9*num_images, 9))

img = tile_raster_images(X_array, image_dims, (1, 1), (1, 1))
axs[0].imshow(img, cmap=cm.nipy_spectral)  # cmap=cm.binary

for i in range(num_steps):
    img = tile_raster_images(np.array([R[i]]), image_dims, (1, 1), (1, 1))
    axs[1 + i].imshow(img, cmap=cm.nipy_spectral)
    pot_en_of_image = f_pot_en(single_X, cast_array_to_local_type(np.array([single_z_evolution[i]])))[0]
    axs[1 + i].set_title('Pot. energy: ' + str(pot_en_of_image), fontsize=32)

Mean loss for this X:  175.627914429
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [67]: 
dim1 = 0
dim2 = 1
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [68]: 
number_images_per_axis = 10
resolution_per_image = 19  # must be an odd number
x_range = .5
y_range = .5

resolution = number_images_per_axis * resolution_per_image
z_sample_final_mean = z_sample_mean[m.n_hmc_steps]
lower_dim1_limit = z_sample_final_mean[dim1] - 0.5*x_range
upper_dim1_limit = z_sample_final_mean[dim1] + 0.5*x_range
lower_dim2_limit = z_sample_final_mean[dim2] - 0.5*y_range
upper_dim2_limit = z_sample_final_mean[dim2] + 0.5*y_range

latent_array = np.zeros((number_images_per_axis**2, n_latents))

pot_energy_matrix = np.zeros((resolution, resolution), dtype='float32')
x = np.linspace(lower_dim1_limit, upper_dim1_limit, resolution)
y = np.linspace(lower_dim2_limit, upper_dim2_limit, resolution)
for i in range(resolution):
    for j in range(resolution):
        #pos_array = f_z_init_mean(single_X)
        pos_array = np.array([z_sample_final_mean])
        pos_array[0, dim1] = x[i]
        pos_array[0, dim2] = y[j]
        pos_array_of_local_type = cast_array_to_local_type(pos_array)
        pot_energy_matrix[j, i] = f_pot_en(single_X, pos_array_of_local_type)[0]
        if i % resolution_per_image == (resolution_per_image - 1)/2 and j % resolution_per_image == (resolution_per_image - 1)/2:
            latent_array[(i//resolution_per_image) + (number_images_per_axis - 1 - j//resolution_per_image)*number_images_per_axis , :] = pos_array[0, :]

        
print 'Minimum potential energy (at grid points): ' + str(pot_energy_matrix.min())
print 'Maximum potential energy (at grid points): ' + str(pot_energy_matrix.max())

fig, axs = plt.subplots(1, 1, figsize=(15, 15))
CS = axs.contour(x, y, pot_energy_matrix, 40)
plt.clabel(CS, inline=1, fmt='%1.1f', fontsize=10, colors=None)  # colors='black'

F = f_gen_rate(cast_array_to_local_type(latent_array))
img = tile_raster_images(F, image_dims, (number_images_per_axis, number_images_per_axis), (1, 1))

axs.imshow(img, cmap=cm.binary, extent=(x.min(), x.max(), y.min(), y.max()))
axs.set_title('Potential energy surface')
plt.show()

Minimum potential energy (at grid points): 172.034
Maximum potential energy (at grid points): 309.269
In [69]: 
resolution = 50
underlying_variance = f_v_init_var(single_X)
velocity_range_for_images = 10.0 * np.sqrt(underlying_variance[0, :])
lower_dim1_limit = np.around(- velocity_range_for_images[dim1])
upper_dim1_limit = np.around(  velocity_range_for_images[dim1])
lower_dim2_limit = np.around(- velocity_range_for_images[dim2])
upper_dim2_limit = np.around(  velocity_range_for_images[dim2])

kin_energy_matrix = np.zeros((resolution, resolution), dtype='float32')
kin_x = np.linspace(lower_dim1_limit, upper_dim1_limit, resolution)
kin_y = np.linspace(lower_dim2_limit, upper_dim2_limit, resolution)
for i in range(resolution):
    for j in range(resolution):
        vel_array = np.zeros((1, m.n_latent)).astype('float32')
        vel_array[0, dim1] = kin_x[i]
        vel_array[0, dim2] = kin_y[j]
        vel_array_of_local_type = cast_array_to_local_type(vel_array)
        kin_energy_matrix[j, i] = f_kin_en(single_X, vel_array_of_local_type)

print 'Minimum kinetic energy (at grid points): ' + str(kin_energy_matrix.min())
print 'Maximum kinetic energy (at grid points): ' + str(kin_energy_matrix.max())

fig, ax = plt.subplots(1, 1, figsize=(9, 9))
CS = ax.contour(kin_x, kin_y, kin_energy_matrix)
#plt.axes().set_aspect('equal', 'datalim')
plt.clabel(CS, inline=1, fmt='%1.1f', fontsize=10)
ax.set_title('Kinetic energy surface')
plt.show()

Minimum kinetic energy (at grid points): 1.07328
Maximum kinetic energy (at grid points): 111.322
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [70]: 
fig, axs = plt.subplots(m.n_hmc_steps + 1, 3, figsize=(18, (m.n_hmc_steps + 1) * 6))
colors = cm.jet(np.linspace(0, 1, 10))

#contour_levels = (198, 200, 202, 204, 206, 208, 210)
#contour_levels = (120, 130, 140, 150, 160, 180, 200, 240, 280)
#contour_levels = (100, 102, 104, 106, 108, 110, 115, 120, 125, 130)
#contour_levels = (400, 402, 404, 406, 408, 410, 412, 416, 420)
#contour_levels = (106, 108, 110, 112, 114, 116, 118, 120, 124, 128)
#contour_levels = (160, 165, 170, 175, 180, 185, 190, 195, 200, 210, 220, 230, 240, 250, 270, 300)
#contour_levels = (174, 175, 176, 177, 178, 180, 182, 184, 186, 190, 200)
#contour_levels = (59, 61, 63, 65, 67, 69, 71, 73, 75, 80, 85, 90)
contour_levels = 40

vel_contour_levels = np.linspace(2.0, 70.0, 18)
#CS0 = axs[0, 0].contourf(x, y, pot_energy_matrix, np.linspace(155, 240, 500))

def colour_for_z_samples(samples):
    mean = samples.mean(axis=0)
    mean1 = mean[dim1]
    mean2 = mean[dim2]
    colour = np.zeros_like(samples[:, 0])
    colour[np.logical_and(samples[:, dim1] < mean1,  samples[:, dim2] < mean2)] = 0
    colour[np.logical_and(samples[:, dim1] < mean1,  samples[:, dim2] >= mean2)] = 2
    colour[np.logical_and(samples[:, dim1] >= mean1, samples[:, dim2] < mean2)] = 4
    colour[np.logical_and(samples[:, dim1] >= mean1, samples[:, dim2] >= mean2)] = 7
    colour[((samples[:, dim1] - mean1) ** 2 + (samples[:, dim2] - mean2) ** 2) < 1e-5] = 9
    return colour.astype('int32')

for i in range(m.n_hmc_steps + 1):
    CS = axs[i, 0].contour(x, y, pot_energy_matrix, contour_levels)
    plt.clabel(CS, inline=1, fmt='%1.0f', fontsize=10)
    axs[i, 0].scatter(z_samples[i,:,dim1], z_samples[i,:,dim2], c=colors[colour_for_z_samples(z_samples[i,:,:])], s=20, alpha=.3, lw=0)
    
    CS_vel = axs[i, 1].contour(kin_x, kin_y, kin_energy_matrix, vel_contour_levels)
    plt.clabel(CS_vel, inline=1, fmt='%1.1f', fontsize=10)
    axs[i, 1].scatter(v_samples[i,:,dim1], v_samples[i,:,dim2], c=colors[colour_for_z_samples(z_samples[i,:,:])], s=20, alpha=.3, lw=0)
    
    pot_energy_distrib = f_pot_en(repeated_X, cast_array_to_local_type(z_samples[i, :, :]))
    if i == 0:
        max_x_value_for_hist = pot_energy_distrib.max() + 5
        min_x_value_for_hist = np.floor(pot_energy_matrix.min()) -5
    pot_energy_distrib_mean = pot_energy_distrib.mean()
    axs[i, 2].hist(pot_energy_distrib, 30, normed=1, range=(min_x_value_for_hist, max_x_value_for_hist))
    axs[i, 2].autoscale(enable=False, axis='both')
    axs[i, 2].axvline(pot_energy_distrib_mean, color='r', linestyle='dashed', linewidth=2)
    axs[i, 2].set_xlim(min_x_value_for_hist, max_x_value_for_hist)
    axs[i, 2].text(pot_energy_distrib_mean + 1.0, 0.8*axs[i, 2].get_ylim()[1], 'Mean: ' + str(pot_energy_distrib_mean))
    axs[i, 1].set_xlim(-velocity_range_for_images[dim1], velocity_range_for_images[dim1])
    axs[i, 1].set_ylim(-velocity_range_for_images[dim2], velocity_range_for_images[dim2])
    axs[i, 1].set_aspect('equal', 'datalim')
    axs[i, 0].set_aspect('equal', 'datalim')

axs[0, 0].scatter(f_z_init_mean(single_X)[0, dim1], f_z_init_mean(single_X)[0, dim2], c='black', s=20)

plt.show()
In [None]: 
z_pos = cast_array_to_local_type(np.array([z_sample_mean[m.n_hmc_steps]])) # [z_sample_mean[3]]

second_deriv0 = f_pot_en_2nd_deriv0(single_X, z_pos)
second_deriv1 = f_pot_en_2nd_deriv1(single_X, z_pos)
second_deriv = np.concatenate([second_deriv0, second_deriv1], axis=0)
det = np.linalg.det(second_deriv)
trace = np.trace(second_deriv)

if trace >= 0 and det >= 0:
    eigvalstring = '+ +'
elif det < 0:
    eigvalstring = '+ -'
else:  # so trace < 0 and det >= 0
    eigvalstring = '- -'

print 'Potential energy:'
print f_pot_en(single_X, z_pos)
print
print '1st derivative:'
print f_pot_en_deriv(single_X, z_pos)
print
print '2nd derivative:'
print second_deriv
print
print '2nd deriv. eigenvalue signs: ', eigvalstring
In [None]: 
#debugprint(f_z1_by_z0.theano_func.theano_func)
zposss = cast_array_to_local_type(np.array([single_z_evolution[0]]))
print f_z1_by_z0(single_X, zposss, zposss)
print f_zT_by_z0(single_X, zposss, zposss)
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [116]: 
np.random.seed(1)

velocity_noise = cast_array_to_local_type(np.random.normal(size=(m.n_hmc_steps, 1, m.n_latent)))
#velocity_noise = np.zeros_like(velocity_noise)
f_z_init_sample
init_pos = f_z_init_sample(single_X) # f_z_init_mean(single_X) # + np.array([0.0, 0.1])
init_vel = f_kin_energy_sample_from_noise(single_X, velocity_noise[0])

num_vels_per_hmc = (m.n_lf_steps + 2)
position_array = np.zeros((m.n_hmc_steps * m.n_lf_steps + 1, m.n_latent))
position_array[0] = init_pos
velocity_array = np.zeros((m.n_hmc_steps * num_vels_per_hmc, m.n_latent))
velocity_array[0] = ma.assert_numpy(init_vel)

for hmc_num in range(m.n_hmc_steps):
    if hmc_num == 0:
        curr_pos = cast_array_to_local_type(init_pos)
        curr_vel = init_vel
    else:
        curr_vel = f_updated_vel_from_noise(single_X, curr_vel, velocity_noise[hmc_num])
        velocity_array[hmc_num * (m.n_lf_steps + 2)] = ma.assert_numpy(curr_vel)
    
    lf_step_results = f_perform_lf_steps(single_X, curr_pos, curr_vel)
    pos_steps = lf_step_results[:m.n_lf_steps]
    vel_half_steps_and_final = lf_step_results[m.n_lf_steps:]
    final_vel = lf_step_results[-1]
    final_pos = pos_steps[-1]
    
    position_array[hmc_num * m.n_lf_steps + 1: (hmc_num + 1)*m.n_lf_steps + 1] = ma.assert_numpy(pos_steps[:, 0, :])
    velocity_array[hmc_num * num_vels_per_hmc + 1: (hmc_num + 1) * num_vels_per_hmc] = ma.assert_numpy(vel_half_steps_and_final[:, 0, :])
    
    curr_pos = final_pos
    curr_vel = final_vel
In [117]: 
fig, axs = plt.subplots(1, 2, figsize=(18, 9))
step_color = cm.jet(np.linspace(0, 1, position_array.shape[0]))
CS = axs[0].contour(x, y, pot_energy_matrix, 40)
CS_vel = axs[1].contour(kin_x, kin_y, kin_energy_matrix, vel_contour_levels)
hmc_step_indices = np.arange(0, position_array.shape[0], m.n_lf_steps)
size_array = 40*np.ones((position_array.shape[0],))
size_array[hmc_step_indices] = 100
axs[0].scatter(position_array[:, dim1], position_array[:, dim2], c=step_color, lw=1, s=size_array)
axs[1].set_color_cycle(step_color)

for hmc_num in range(m.n_hmc_steps):
    curr_vel_range = np.arange(num_vels_per_hmc * hmc_num, num_vels_per_hmc * (hmc_num + 1) - 2)
    init_vel_ind = hmc_num * num_vels_per_hmc
    final_vel_ind = (hmc_num + 1) * num_vels_per_hmc - 1
    curr_index = hmc_step_indices[hmc_num]
    next_index = hmc_step_indices[hmc_num + 1]
    for j in curr_vel_range:
        axs[1].plot(velocity_array[j:j+2, dim1], velocity_array[j:j+2, dim2], lw=2)
    axs[1].scatter(velocity_array[init_vel_ind, dim1], velocity_array[init_vel_ind, dim2], c=step_color[curr_index], lw=0, s=100)
    axs[1].scatter(velocity_array[final_vel_ind, dim1], velocity_array[final_vel_ind, dim2], c=step_color[next_index], lw=0, s=100)

for hmc_num in range(m.n_hmc_steps):
    final_vel_ind = (hmc_num + 1) * num_vels_per_hmc - 1
    next_index = hmc_step_indices[hmc_num + 1]
    axs[1].plot(velocity_array[final_vel_ind-1:final_vel_ind+1, dim1], velocity_array[final_vel_ind-1:final_vel_ind+1, dim2], lw=2, c=step_color[next_index])

axs[0].set_aspect('equal', 'datalim')
axs[1].set_aspect('equal', 'datalim')
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [118]: 
inv_model_mean_output = np.zeros((m.n_hmc_steps, m.n_latent, num_repeats, m.n_latent))
inv_model_var_output = np.zeros((m.n_hmc_steps, m.n_latent, num_repeats, m.n_latent))

for i in range(m.n_hmc_steps):
    variation_start = z_sample_mean[i] - 2*z_sample_std[i]
    variation_end = z_sample_mean[i] + 2*z_sample_std[i]
    
    time_array = cast_array_to_local_type(np.array([i]).astype('float32'))
    
    for variation_dim in range(m.n_latent):
        z_variation = np.linspace(variation_start[variation_dim], variation_end[variation_dim], num_repeats)
        sample_array = np.tile(z_sample_mean[i], (num_repeats, 1))
        sample_array[:, variation_dim] = z_variation
        local_type_sample_array = cast_array_to_local_type(sample_array)
        if 'velocity' not in m.auxiliary_inv_model_inpt:
            inv_model_mean_output[i, variation_dim] = f_aux_inv_mean(repeated_X, local_type_sample_array, time_array)
            inv_model_var_output[i, variation_dim] = f_aux_inv_var(repeated_X, local_type_sample_array, time_array)
        else:
            velocity_array = 0.0 * local_type_sample_array
            inv_model_mean_output[i, variation_dim] = f_aux_inv_mean(repeated_X, local_type_sample_array, velocity_array, time_array)
            inv_model_var_output[i, variation_dim] = f_aux_inv_var(repeated_X, local_type_sample_array, velocity_array, time_array)
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [122]: 
variation_start = z_sample_mean[m.n_hmc_steps] - 2*z_sample_std[m.n_hmc_steps]
variation_end = z_sample_mean[m.n_hmc_steps] + 2*z_sample_std[m.n_hmc_steps]
print variation_start
print variation_end
final_vel_model_mean_output = np.zeros((m.n_latent, num_repeats, m.n_latent))
final_vel_model_var_output = np.zeros((m.n_latent, num_repeats, m.n_latent))

for variation_dim in range(m.n_latent):
    z_variation = np.linspace(variation_start[variation_dim], variation_end[variation_dim], num_repeats)
    sample_array = np.tile(z_sample_final_mean, (num_repeats, 1))
    sample_array[:, variation_dim] = z_variation
    final_vel_model_mean_output[variation_dim] = f_v_final_mean(repeated_X, cast_array_to_local_type(sample_array))
    final_vel_model_var_output[variation_dim] = f_v_final_var(repeated_X, cast_array_to_local_type(sample_array))

[ 0.21006711 -0.56645823]
[ 0.30517325 -0.45014334]
In [123]: 
fig, axs = plt.subplots(m.n_hmc_steps, 2, figsize=(18, 9*m.n_hmc_steps))

for i in range(m.n_hmc_steps - 1):
    axs[i, 0].scatter(inv_model_mean_output[i+1, :, :, dim1], 
           inv_model_mean_output[i+1, :, :, dim2],  
           c=np.transpose(np.tile(np.linspace(0, m.n_latent-1, m.n_latent), (num_repeats, 1))), 
           lw=0, s=5)
    axs[i, 1].scatter(inv_model_var_output[i+1, :, :, dim1], 
           inv_model_var_output[i+1, :, :, dim2],  
           c=np.transpose(np.tile(np.linspace(0, m.n_latent-1, m.n_latent), (num_repeats, 1))), 
           lw=0, s=5)
    axs[i, 0].set_title('Aux. inv. model ' + str(i+1) + ': Mean')
    axs[i, 1].set_title('Aux. inv. model ' + str(i+1) + ': Variance')
        
if m.n_hmc_steps == 1:
    axs[0].scatter(final_vel_model_mean_output[:, :, dim1], 
               final_vel_model_mean_output[:, :, dim2],  
               c=np.transpose(np.tile(np.linspace(0,m.n_latent-1,m.n_latent), (num_repeats, 1))), 
               lw=0, s=5)
    axs[1].scatter(final_vel_model_var_output[:, :, dim1], 
               final_vel_model_var_output[:, :, dim2],  
               c=np.transpose(np.tile(np.linspace(0,m.n_latent-1,m.n_latent), (num_repeats, 1))), 
               lw=0, s=5)
    axs[0].set_title('Final vel. model: Mean')
    axs[1].set_title('Final vel. model: Variance')
else:
    axs[m.n_hmc_steps-1, 0].scatter(final_vel_model_mean_output[:, :, dim1], 
               final_vel_model_mean_output[:, :, dim2],  
               c=np.transpose(np.tile(np.linspace(0,m.n_latent-1,m.n_latent), (num_repeats, 1))), 
               lw=0, s=5)
    axs[m.n_hmc_steps-1, 1].scatter(final_vel_model_var_output[:, :, dim1], 
               final_vel_model_var_output[:, :, dim2],  
               c=np.transpose(np.tile(np.linspace(0,m.n_latent-1,m.n_latent), (num_repeats, 1))), 
               lw=0, s=5)
    axs[m.n_hmc_steps-1, 0].set_title('Final vel. model: Mean')
    axs[m.n_hmc_steps-1, 1].set_title('Final vel. model: Variance')

plt.show()
In [None]: 
print v_samples[0, :, :].mean(axis=0)
print v_samples[1, :, :].mean(axis=0)
print v_samples[2, :, :].mean(axis=0)
print v_samples[3, :, :].mean(axis=0)
print
print v_samples[0, :, :].var(axis=0)
print v_samples[1, :, :].var(axis=0)
print v_samples[2, :, :].var(axis=0)
print v_samples[3, :, :].var(axis=0)
In [None]: 
final_z_samples = cast_array_to_local_type(z_samples[m.n_hmc_steps, :, :])
final_v_samples = cast_array_to_local_type(v_samples[m.n_hmc_steps, :, :])
final_vel_mean = f_v_final_mean(repeated_X, final_z_samples)
final_vel_var = f_v_final_var(repeated_X, final_z_samples)
final_vel_nll = f_v_final_model_nll(repeated_X, final_z_samples, final_v_samples)
In [None]: 
print f_kin_energy_nll(single_X).sum(-1)

print final_vel_nll.mean()
print final_vel_nll.min()
print final_vel_nll.max()
In [None]: 
#m.parameters.view(m.auxiliary_inv_model.mlp.layers[2].weights)
print m.parameters._var_to_slice[m.auxiliary_inv_model.mlp.layers[2].weights]
#grad[594190:594990]
#old_weights_array = m.parameters.view(m.auxiliary_inv_model.mlp.layers[0].weights)
#new_array = old_weights_array.copy()
#new_array[-1, :] = 1.0 + old_weights_array[-1, :]
#m.parameters.__setitem__(m.auxiliary_inv_model.mlp.layers[0].weights, new_array)
print m.parameters.view(m.auxiliary_inv_model.mlp.layers[2].weights).shape
In [None]: 
np.set_printoptions(suppress=True)
print np.around(np.reshape(mean_grad[396390:553790], (787, 200)), 5)[:198]  # 396390:553790
np.reshape(mean_grad[594190:594990], (200, 4))  # 396390:553790
#print np.around(np.reshape(m.parameters.data[396390:553790].astype('float32'), (787, 200)), 5)[:50]
Node Commands Syntax: node {operator} [options] [arguments] Parameters: /? or /help - Display this help message. list - List nodes or node history or the cluster listcores - List cores on the cluster view - View properties of a node online - Set nodes or node to online state offline - Set one or more nodes to the offline state For more information about HPC command-line tools, see http://go.microsoft.com/fwlink/?LinkId=120724.
In [None]: 
fig, axs = plt.subplots(4, 2, figsize=(18, 36))
# TODO: Analysis of how final_vel_mean and final_vel_var depend on z (since they all share the same x)

print z_samples[3, :, :].mean(axis=0)
print z_samples[3, :, :].var(axis=0)
print v_samples[3, :, :].mean(axis=0)
print v_samples[3, :, :].var(axis=0)
print f_v_init_var(np.array([X[X_index, :]]))

print final_vel_nll.mean()
plt.boxplot(final_vel_nll, whis=1)
plt.show()
In [None]: 
centers = np.zeros((10,n_latents))
stddevs = np.zeros((10,n_latents))
centers_init = np.zeros((10,n_latents))
stddevs_init = np.zeros((10,n_latents))
for i in range(10):
    Li = f_z_sample(X[Z.argmax(1) == i])
    centers[i] = Li.mean(axis=0)
    stddevs[i] = np.std(Li, axis=0)
    
    Li_init = f_z_init_sample(X[Z.argmax(1) == i])
    centers_init[i] = Li_init.mean(axis=0)
    stddevs_init[i] = np.std(Li_init, axis=0)
In [None]: 
fig, axs = plt.subplots(1, 2, figsize=(18, 9))
axs[0].scatter(centers[:, dim1], centers[:, dim2], c=range(10), s=50)
axs[0].scatter(centers_init[:, dim1], centers_init[:, dim2], c=range(10), s=50, marker=u's')

axs[1].scatter(centers[:, dim1], centers[:, dim2], c=range(10), s=50)
axs[1].scatter(centers[:, dim1] + stddevs[:, dim1], centers[:, dim2], c=range(10), s=50, marker=u'>')
axs[1].scatter(centers[:, dim1] - stddevs[:, dim1], centers[:, dim2], c=range(10), s=50, marker=u'<')
axs[1].scatter(centers[:, dim1], centers[:, dim2] + stddevs[:, dim2], c=range(10), s=50, marker=u'^')
axs[1].scatter(centers[:, dim1], centers[:, dim2] - stddevs[:, dim2], c=range(10), s=50, marker=u'v')

#axs[0].set_xlim(-1.2, 1.2)
#axs[0].set_ylim(-1.2, 1.2)
#axs[1].set_xlim(-1.2, 1.2)
#axs[1].set_ylim(-1.2, 1.2)

print (centers[:, dim1] - centers_init[:, dim1])
print (centers[:, dim2] - centers_init[:, dim2])
print (stddevs[:, dim1] - stddevs_init[:, dim1])
print (stddevs[:, dim2] - stddevs_init[:, dim2])
In [None]: